Optimal Robust Real-time Pricing Algorithm Based on Utility Maximization for Smart Grid

In this paper, the robust real-time pricing problem is considered. We consider that the optimization problem used for describing the pricing process contains uncertain parameters, such as the type parameter, which may be unknown or only partially known by each agent during the price setting stage. To deal with such a realistic problem, we propose a robust real-time pricing model based on utility maximization and formulate the whole problem as a robust optimization problem. In the formulated optimization problem, the worst-case utility is maximized while the constraints should be satisfied for any possible realization of the uncertain parameters. In this paper, we adopt two widely-used utility functions, the quadratic utility function and Logarithmic utility function respectively, and give the strategies to obtain optimal robust real-time price for both of these two cases. Simulation results are presented to show the performance of the proposed robust pricing method.